Polynuclear growth on a flat substrate and edge scaling of GOE eigenvalues
Polynuclear growth on a flat substrate and edge scaling of GOE eigenvalues
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DOI：
10.1007/s00220-004-1204-6
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发表时间：
2004-12-01
影响因子：
2.4
通讯作者：
Ferrari, PL
中科院分区：
文献类型：
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作者：
Ferrari, PL
我们考虑具有平坦初始条件和无附加约束的1+1维多核生长（PNG）模型。通过RSK （Robinson-Schensted-Knuth）构造得到多层PNG模型，该模型由一堆不相交的线组成，最上面的线是PNG高度。线的统计量是平移不变的，在固定的位置上，线定义了一个点过程。我们证明了在大倍的情况下，这个点的边缘经过适当的缩放，是有极限的。这一极限是一个普氏点过程，与随机矩阵高斯正交系综（GOE）的边缘缩放过程相同。我们的研究结果进一步揭示了KPZ类1+1维增长模型的普适结构。
We consider the polynuclear growth (PNG) model in 1+1 dimension with flat initial condition and no extra constraints. Through the Robinson-Schensted-Knuth (RSK) construction, one obtains the multilayer PNG model, which consists of a stack of non-intersecting lines, the top one being the PNG height. The statistics of the lines is translation invariant and at a fixed position the lines define a point process. We prove that for large times the edge of this point process, suitably scaled, has a limit. This limit is a Pfaffian point process and identical to the one obtained from the edge scaling of the Gaussian orthogonal ensemble (GOE) of random matrices. Our results give further insight to the universality structure within the KPZ class of 1+1 dimensional growth models.